Independent Component Analysis and Non-Gaussian Inferential Metrics in Geophysical Sciences

Publication briefs

Publication type: Research Monograph [Dissertation]
Author: Rui A. Pita Perdigão (R.A.P. Perdigão)
Date: July 2004
Title: Independent Component Analysis of the low frequency Geopotential Height Field and its relevance to Precipitation regimes over the Euro-Atlantic region.
Cite as: Perdigão, Rui A. P. (2004): Independent Component Analysis of the low frequency Geopotential Height Field and its relevance to Precipitation regimes over the Euro-Atlantic region.
Indexed: Yes (Crossref)

Methodological Keywords: Complex Systems, Dynamical Systems, Information Theory, Information Physics, Fluid Dynamics, Predictability, Mathematical Physics, Dynamical Systems, Independent Component Analysis, Non-Gaussian Inference.
Applied Keywords: Geopotential Height Fields, Precipitation, Euro-Atlantic, Meteorology, Oceanography, Geophysical Sciences.

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Independent Component Analysis (ICA) is a data analysis technique suitable for revealing hidden factors that underlie sets of random variables, measurements, or signals.
It does so by transforming a multidimensional random vector into components whose statistical dependence from each other is minimised, i.e., that are as close to statistical independence from each other as possible. There exist a wide variety of feature extraction methods, depending on the applied criteria, e.g. PCA maximises variance for a given inner product. ICA searches for statistically independent components, in the general case where the data is non-Gaussian.

Some other approaches such as factor analysis methods are optimal only when data have a Gaussian distribution, thus evaluating independence through uncorrelatedness. That could make sense, since for Gaussian data uncorrelated components are always independent. In reality, though, the data may not follow a Gaussian distribution. When that happens, a null Correlation between the components is not enough to ensure their independence.
Statistical independence means that the value of any of the components gives no information on the values of other components, and therefore the predictability potential of one variable from another one is null. That implies uncorrelatedness, but not vice-versa (i.e. uncorrelatedness does not imply independence, in general).

Seen this, ICA has obvious advantages over the referred methods as far as non-Gaussian signals are concerned.

The present work envisions a contribution to the establishment of the grounds for the search for independent components within the atmospheric phenomena, so that it may be possible to deepen the understanding of the fundamental tools that may allow us to extract relevant independent information from the data, thus being able to analyse each factor independently, therefore with increased ease.

For that purpose, this work adapts and applies ICA to the analysis of Geopotential Height Field data, not before diagnosing non-Gaussianity within the data, so as to check the applicability of the method and determine important features of the data itself.
More specifically, it shall be put in evidence the existence of moderately robust independent components in the low frequency Geopotential Height variability, and the evidence of regimes, particularly bimodality, within the data. Furthermore, the present work shall search for extra relationships – beyond the linear correlation – between the independent components and climatic variables such as the Monthly Cumulated Precipitation. That way, it shall be possible to get a new insight on the statistical relationships between the Geopotential Height Field and Precipitation regimes, within the considered circumstances.